# Mathematical relationship between frequency and time period

### What is the relationship between frequency and period? - The Handy Physics Answer Book

The wavelength and frequency of light are closely related. The higher the frequency, the shorter the wavelength. Because all light waves move through a. is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency. Frequency, f, is how many cycles of an oscillation occur per second and is The period of a wave, T, is the amount of time it takes a wave to vibrate one full.

This is an electronic instrument which measures the frequency of an applied repetitive electronic signal and displays the result in hertz on a digital display. It uses digital logic to count the number of cycles during a time interval established by a precision quartz time base.

## Frequency and Period of a Wave

Cyclic processes that are not electrical in nature, such as the rotation rate of a shaft, mechanical vibrations, or sound wavescan be converted to a repetitive electronic signal by transducers and the signal applied to a frequency counter. This represents the limit of direct counting methods; frequencies above this must be measured by indirect methods. Heterodyne methods[ edit ] Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly by means of heterodyning frequency conversion.

A reference signal of a known frequency near the unknown frequency is mixed with the unknown frequency in a nonlinear mixing device such as a diode. This creates a heterodyne or "beat" signal at the difference between the two frequencies. If the two signals are close together in frequency the heterodyne is low enough to be measured by a frequency counter.

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This process only measures the difference between the unknown frequency and the reference frequency. To reach higher frequencies, several stages of heterodyning can be used.

Current research is extending this method to infrared and light frequencies optical heterodyne detection. In that lesson, it was mentioned that a wave is created in a slinky by the periodic and repeating vibration of the first coil of the slinky.

## Mathematical relation between frequency and time period of a sound wave

This vibration creates a disturbance that moves through the slinky and transports energy from the first coil to the last coil. A single back-and-forth vibration of the first coil of a slinky introduces a pulse into the slinky. But the act of continually vibrating the first coil with a back-and-forth motion in periodic fashion introduces a wave into the slinky. Suppose that a hand holding the first coil of a slinky is moved back-and-forth two complete cycles in one second.

The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium.

Frequency is a part of our common, everyday language. For example, it is not uncommon to hear a question like "How frequently do you mow the lawn during the summer months? If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz.

### Wavelength, Period,Frequency

If a coil of slinky makes 3 vibrational cycles in one second, then the frequency is 3 Hz. The quantity frequency is often confused with the quantity period.

Period refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period.

The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years.